How do I calculate the length of a bond?

[fizzicsdummy]

“In C6H8, the carbon atoms are connected in a chain. In a rough approximation, some electrons can be viewed as confined to a line with the length of this chain. C6H8 absorbs ultraviolet light with wavelength 357 nm, which causes an electron to change from the third lowest allowed energy to the fourth lowest allowed energy. Use this information to estimate the length in pm of a typical carbon-carbon bond in C6H8.”

I assume I could just calculate the radius of a carbon atom and multiply it by 2 to find a rough estimate of the length of a carbon-carbon bond. However, I don't know how to do this and I don't know the importance of the energy level change described in the problem. I'd really appreciate help understanding this. An equation (if one exists) would also be appreciated. I do know that radius = (n^2)(Bohr radius). Thanks!

 

[GCT]

“In C6H8, the carbon atoms are connected in a chain. In a rough approximation, some electrons can be viewed as confined to a line with the length of this chain. C6H8 absorbs ultraviolet light with wavelength 357 nm, which causes an electron to change from the third lowest allowed energy to the fourth lowest allowed energy. Use this information to estimate the length in pm of a typical carbon-carbon bond in C6H8.”

I assume I could just calculate the radius of a carbon atom and multiply it by 2 to find a rough estimate of the length of a carbon-carbon bond. However, I don't know how to do this and I don't know the importance of the energy level change described in the problem. I'd really appreciate help understanding this. An equation (if one exists) would also be appreciated. I do know that radius = (n^2)(Bohr radius). Thanks!

You can estimate the length of the bond by referring to the typical bond energies of carbon - carbon bonds e.g. single , double , triple and compare these with the energy of the wavelength given to you.

The other way is by using the Particle In a Box theory , this is better than using the Bohr model , however it depends on which class you are in.

 

[Blueshift5]

To calculate the length of a bond, we need to use the concept of bond length, which is defined as the distance between the nuclei of two bonded atoms. This distance is determined by the balance between attractive and repulsive forces between the atoms.

In the case of C6H8, the absorption of ultraviolet light causes an electron to change from the third lowest allowed energy level to the fourth lowest allowed energy level. This energy level change is related to the bond length, as a shorter bond would require a higher energy to promote an electron to a higher energy level.

To estimate the length of a carbon-carbon bond in C6H8, we can use the equation for the Bohr radius, which is given by r = (n^2)(a0) where n is the principle quantum number and a0 is the Bohr radius (0.529 Å).

Since the electron is moving from the third to the fourth energy level, n = 4. Plugging this into the equation, we get r = (4^2)(0.529 Å) = 8.464 Å.

However, this is only an estimate and does not take into account the actual bond length in C6H8. To get a more accurate value, we would need to use experimental data or more advanced calculations. Additionally, the length of a bond can vary depending on the specific molecule and its environment, so it is important to keep in mind that this is just an approximation.